BEC condensate fraction: N₀/N = 1 − (T/Tc)^(3/2); k_B·Tc = 2π·ℏ²·n^(2/3)/(m·ζ(3/2)^(2/3))

BEC condensate fraction and critical temperature. Using framework F8 (polylog thermodynamic integrals), the thermal-cloud density above Tc equals n·λ_T³ = g_{3/2}(z); at the transition z = 1 gives n_c·λ_Tc³ = ζ(3/2). Solving for Tc: k_B·Tc…